Mathematics, 21.07.2020 06:01 ari313

Consider a cupcake shop that sells 7 different kinds of cupcakes (chocolate raspberry, strawberry shortcake, red velvet, funfetti, lemon, German chocolate, and chocolate caramel). Assuming there are at least 12 of each kind available, if Andres asks for a random selection of 12 cupcakes, what is the probability that he will get (a)exactly 6 red velvet?
(b)exactly 3 each of 4 different kinds?
(c)no lemon?
(d)at least 1 German chocolate and at least one chocolate raspberry?

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Answer from: ciaotaylor

If Andres asks for a random selection of 12 cupcakes, the Probability of choosing:

a)exactly 6 red velvet?

The probability that 6 will be red velvet = 6/12 x 14.3% = 7.2%

(b)exactly 3 each of 4 different kinds?

Since 3 x 4 = 12

The probability that the 12 will be 3 each from 4 different kinds

= 14.3%

(c)no lemon?

Probability of getting a lemon cupcake = 1/7 = 14.3%

Therefore, probability of not getting a lemon cupcake = 100% - 14.3% = 85.7%

(d)at least 1 German chocolate and at least one chocolate raspberry?

The probability of at least 2 being 1 German and 1 chocolate raspberry

= 2/12

= 16.67%

Step-by-step explanation:

a) Probability of each kind of Cupcake

Kind of Cupcakes Quantity Probability

chocolate raspberry 12 14.285%

strawberry shortcake 12 14.3%

red velvet 12 14.3%

funfetti 12 14.3%

lemon 12 14.3%

German chocolate 12 14.3%

chocolate caramel 12 14.3%

b) The probability of choosing a kind of cupcake is the chance that, for example, a strawberry cupcake is chosen instead of the other six kinds. It expresses the opportunity that an event has in happening out of many other events that could have happened.

Answer from: Quest

The answer would be (c)

Answer from: Quest

$7.00 \cdot 10^{-7} m - 1\cdot 10^{-3} m$

explanation:

infrared radiation has wavelength in the range between 700 nm and 1 mm. lets' convert these values into scientific notation, keeping in mind that:

$1 nm = 10^{-9} m\\1 mm = 10^{-3} m$

let's start from the lower value, we have:

$700 nm = 700 \cdot 10^{-9} m = 7.00 \cdot 10^{-7} m$ (we moved the dot two places to the left, so we increased the exponent by 2 units, from -9 to -7)

the higher value is:

$1 mm = 1 \cdot 10^{-3} m$

so, the range of wavelength of infrared radiation is:

$7.00 \cdot 10^{-7} m - 1\cdot 10^{-3} m$

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